[F(x):=,B(k):=]

;Sub(User')
M(k,x,h):=IF(k=1,-F(x+h)/(2*h)-F(x)/(2*h)+INT(F(y),y,x,x+h)/h^2,B(2*k-2)*(LIM~
(DIF(F(y),y,2*k-3),y,x+h,0)-LIM(DIF(F(y),y,2*k-3),y,x,0))/(h^2*(2*k-2)!)+M(k-~
1,x,h)/h^2)

(F(x+h)+F(x))/2=INT(F(y),y,x,x+h)/h+SUM(h^(2*k-1)*B(2*k)*(LIM(DIF(F(y),y,2*k-~
1),y,x+h,0)-LIM(DIF(F(y),y,2*k-1),y,x,0))/(2*k)!,k,1,l)-h^(2*l+1)*M(l+1,x,h)

l=12

;Simp(Sub(#3))
true